US6428203B1ExpiredUtility
Power compensation differential scanning calorimeter
Est. expiryMar 23, 2020(expired)· nominal 20-yr term from priority
Inventors:Robert L. Danley
G01N 25/4833G01K 17/00G01K 17/04G01N 25/4866
92
PatentIndex Score
59
Cited by
29
References
66
Claims
Abstract
A power compensation differential scanning calorimeter that uses one absolute temperature measurement, two differential temperature measurements, a differential power measurement, and a five-term heat flow equation to measure the sample heat flow. The calorimeter is calibrated by running two sequential calibration experiments. In a preferred embodiment, the first calibration experiment uses empty sample and reference pans, and the second calibration experiment uses sapphire specimens in the sample and reference holders. In an alternate embodiment, sapphire calibration specimens are used in both the first and second calibration experiments.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1. A power compensation differential scanning calorimeter comprising:
(a) an absolute temperature detector which measures one of a sample temperature, a reference temperature, and an isothermal enclosure temperature;
(b) a first differential temperature detector which measures one of the difference between the sample temperature and the isothermal enclosure temperature, the difference between the reference temperature and the isothermal enclosure temperature, and the difference between the sample temperature and the reference temperature;
(c) a second differential temperature detector which measures another one of the difference between the sample temperature and the reference temperature, the difference between the sample temperature and the isothermal enclosure temperature, and the difference between the reference temperature and the isothermal enclosure temperature; and
(d) meters for measuring a differential power to the sample with respect to the reference,
wherein the power compensation calorimeter is calibrated by running a first experiment with an empty cell according to a pre-selected temperature program, and running a second experiment, with a sample calibration specimen in a sample holder and a reference calibration specimen in a reference holder, according to the same pre-selected temperature program.
2. The power compensation differential scanning calorimeter of claim 1 , further comprising means for calculating a sample thermal capacitance according to: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · p s1 Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
3. The power compensation differential scanning calorimeter of claim 1 , further comprising means for calculating a sample thermal resistance according to: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · p s1 .
4. The power compensation differential scanning calorimeter of claim 1 , further comprising means for calculating a reference thermal capacitance according to: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · p r1 ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
5. The power compensation differential scanning calorimeter of claim 1 , further comprising means for calculating a reference thermal resistance according to: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) [ m r2 · C mat · ( T s1 d τ - Δ T 1 d τ ) - p r2 ] · ( T s1 d τ - Δ T 1 d τ ) - p r1 · ( Δ T 2 d τ - T s2 d τ ) .
6. The power compensation differential scanning calorimeter of claim 1 ,
wherein the absolute temperature detector measures the sample temperature, the first differential temperature detector measures the difference between the sample temperature and the isothermal enclosure temperature, and the second differential temperature detector measures the difference between the sample temperature and the reference temperature, and
further comprising means for calculating a differential heat flow to the sample according to: q = Δ p + Δ T o · ( R r - R s R r · R s ) - Δ T R r + ( C r - C s ) · T s d τ - C r · Δ T d τ .
7. A power compensation differential scanning calorimeter comprising:
(a) an absolute temperature detector which measures one of a sample temperature, a reference temperature, and an isothermal enclosure temperature;
(b) a first differential temperature detector which measures one of the difference between the sample temperature and the isothermal enclosure temperature, the difference between the reference temperature and the isothermal enclosure temperature, and the difference between the sample temperature and the reference temperature;
(c) a second differential temperature detector which measures another one of the difference between the sample temperature and the reference temperature, the difference between the sample temperature and the isothermal enclosure temperature, and the difference between the reference temperature and the isothermal enclosure temperature; and
(d) meters for measuring a differential power to the sample with respect to the reference,
wherein the power compensation calorimeter is calibrated by running a first experiment with a first sample calibration specimen in a sample holder and a first reference calibration specimen in a reference holder according to a pre-selected temperature program, and running a second experiment, with a second sample calibration specimen in the sample holder and a second reference calibration specimen in the reference holder, according to the same pre- selected temperature program, wherein the first sample calibration specimen has a mass that is substantially different from the mass of the second sample calibration specimen.
8. The power compensation differential scanning calorimeter of claim 7 , further comprising means for calculating a sample thermal capacitance according to: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · ( p s1 - m s1 · C mat · T s1 d τ ) Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
9. The power compensation differential scanning calorimeter of claim 7 , further comprising means for calculating a sample thermal resistance according to: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · ( p s1 - m s1 · C mat · T s1 d τ ) .
10. The power compensation differential scanning calorimeter of claim 7 , further comprising means for calculating a reference thermal capacitance according to: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
11. The power compensation differential scanning calorimeter of claim 7 , further comprising means for calculating a reference thermal resistance according to: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) ( T s1 d τ - Δ T 1 d τ ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( T s2 d τ - Δ T 2 d τ ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] .
12. The power compensation differential scanning calorimeter of claim 7 ,
wherein the absolute temperature detector measures the sample temperature, the first differential temperature detector measures the difference between the sample temperature and the isothermal enclosure temperature, and the second differential temperature detector measures the difference between the sample temperature and the reference temperature, and
further comprising means for calculating a differential heat flow to the sample according to: q = Δ p + Δ T o · ( R r - R s R r · R s ) - Δ T R r + ( C r - C s ) · T s d τ - C r · Δ T d τ .
13. A method for determining differential heat flow to a sample with respect to a reference in a power compensation differential scanning calorimeter comprising:
(a) calibrating the calorimeter by measuring a sample thermal resistance, a sample thermal capacitance, a reference thermal resistance and a reference thermal capacitance; and
(b) using a five-term heat flow equation to determine the differential heat flow to the sample with respect to the reference.
14. The method of claim 13 , wherein the step of measuring the sample thermal resistance comprises using the equation: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · p s1 .
15. The method of claim 13 , wherein the step of measuring the sample thermal capacitance comprises using the equation: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · p s1 Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
16. The method of claim 13 , wherein the step of measuring the reference thermal resistance comprises using the equation: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) [ m r2 · C mat · ( T s1 d τ - Δ T 1 d τ ) - p r2 ] · ( T s1 d τ - Δ T 1 d τ ) - p r1 · ( Δ T 2 d τ - T s2 d τ ) .
17. The method of claim 13 , wherein the step of measuring the reference thermal capacitance comprises using the equation: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · p r1 ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
18. The method of claim 13 , wherein the step of measuring the sample thermal resistance comprises using the equation: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · ( p s1 - m s1 · C mat · T s1 d τ ) .
19. The method of claim 13 , wherein the step of measuring the sample thermal capacitance comprises using the equation: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · ( p s1 - m s1 · C mat · T s1 d τ ) Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
20. The method of claim 13 , wherein the step of measuring the reference thermal resistance comprises using the equation: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) ( T s1 d τ - Δ T 1 d τ ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( T s2 d τ - Δ T 2 d τ ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] .
21. The method of claim 13 , wherein the step of measuring the reference thermal capacitance comprises using the equation: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
22. The method of claim 13 , comprising storing the sample thermal resistance, sample thermal capacitance, reference thermal resistance, and reference thermal capacitance as tabular data.
23. The method of claim 13 , comprising fitting the sample thermal resistance, sample thermal capacitance, reference thermal resistance, and reference thermal capacitance to a mathematical expression.
24. The method of claim 23 , wherein the mathematical expression is a polynomial.
25. A method for determining differential heat flow to a sample with respect to a reference using a power compensation differential scanning calorimeter comprising:
(a) calibrating the power compensation differential scanning calorimeter by measuring a sample thermal resistance, a sample thermal capacitance, a reference thermal resistance, and a reference thermal capacitance over a first range of temperatures;
(b) placing a sample on a sample holder in the power compensation differential scanning calorimeter;
(c) increasing the temperature of the sample over a second range of temperatures, wherein the second range of temperatures does not exceed the first range of temperatures;
(d) measuring differential power to the sample with respect to the reference, differential temperature between the sample holder and a reference holder, differential temperature between the sample holder and an isothermal enclosure, and a sample temperature; and
(e) determining the differential heat flow to the sample with respect to the reference using a five-term heat flow equation as follows: q = Δ p + Δ T o · ( R r - R s R r · R s ) - Δ T R r + ( C r - C s ) · T s d τ - C r · Δ T d τ
at temperatures within the second range of temperatures.
26. The power compensation differential scanning calorimeter method of claim 25 , wherein the step of measuring the sample thermal capacitance comprises using the equation: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · p s1 Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
27. The power compensation differential scanning calorimeter method of claim 25 , wherein the step of measuring the sample thermal resistance comprises using the equation: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · p s1 .
28. The power compensation differential scanning calorimeter method of claim 25 , wherein the step of measuring the reference thermal capacitance comprises using the equation: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · p r1 ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
29. The power compensation differential scanning calorimeter method of claim 25 , wherein the step of measuring the reference thermal resistance comprises using the equation: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) [ m r2 · C mat · ( T s1 d τ - Δ T 1 d τ ) - p r2 ] · ( T s1 d τ - Δ T 1 d τ ) - p r1 · ( Δ T 2 d τ - T s2 d τ ) .
30. The method of claim 25 , wherein the step of measuring the sample thermal resistance comprises using the equation: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · ( p s1 - m s1 · C mat · T s1 d τ ) .
31. The method of claim 25 , wherein the step of measuring the sample thermal capacitance comprises using the equation: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · ( p s1 - m s1 · C mat · T s1 d τ ) Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
32. The method of claim 25 , wherein the step of measuring the reference thermal resistance comprises using the equation: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) ( T s1 d τ - Δ T 1 d τ ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( T s2 d τ - Δ T 2 d τ ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] .
33. The method of claim 25 , wherein the step of measuring the reference thermal capacitance comprises using the equation: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
34. The method of claim 25 , comprising storing the sample thermal resistance, sample thermal capacitance, reference thermal resistance, and reference thermal capacitance as tabular data.
35. The method of claim 25 , comprising fitting the sample thermal resistance, sample thermal capacitance, reference thermal resistance, and reference thermal capacitance to a mathematical expression.
36. The method of claim 35 , wherein the mathematical expression is a polynomial.
37. A method for measuring the differential heat flow to a sample with respect to a reference using a power compensation differential scanning calorimeter comprising:
(a) calibrating the calorimeter by measuring a sample thermal resistance, a sample thermal capacitance, a reference thermal resistance, and a reference thermal capacitance;
(b) measuring individually a power supplied to a sample holder, a power supplied to a reference holder, an isothermal enclosure temperature, a sample holder temperature, and a reference holder temperature; and
(c) calculating the differential heat flow to the sample with respect to the reference using a six-term equation as follows: q = p s - p r + T o - T s R s - T o - T r R r - C s · T s d τ + C r · T r d τ .
38. A power compensation differential scanning calorimeter comprising:
(a) an isothermal enclosure;
(b) a sample holder installed in the isothermal enclosure and supported by a sample thermal resistor having a small cross-sectional area in the direction normal to the heat flow to the sample holder, wherein the sample holder has a sample temperature detector and a sample heating element, and is adapted to receive a sample;
(c) a reference holder installed in the isothermal enclosure and supported by a reference thermal resistor having a small cross-sectional area in the direction normal to the heat flow to the reference holder, wherein the reference holder has a reference temperature detector and a reference heating element, and is adapted to at receive a reference; and
(d) an isothermal enclosure temperature detector for measuring the isothermal temperature.
39. The power compensation differential scanning calorimeter of claim 38 , wherein the sample temperature detector measures absolute temperature.
40. The power compensation differential scanning calorimeter of claim 38 , wherein the power compensation differential scanning calorimeter measures a first differential temperature between the sample holder and the reference holder, a second differential temperature between the sample holder and the isothermal enclosure, and a differential power between the sample and the reference.
41. The power compensation differential scanning calorimeter of claim 40 , wherein the differential power between the sample and the reference is measured by separately measuring power to the sample holder and power to the reference holder, and calculating a difference between the power to the sample holder and the power to the reference holder.
42. The power compensation differential scanning calorimeter of claim 41 , wherein the power to the sample holder and the power to the reference holder are measured by instrumentation that measures voltages and currents to the sample heating element and the reference heating element.
43. The power compensation differential scanning calorimeter of claim 38 , wherein the isothermal enclosure is cooled and is constructed of a high conductivity material.
44. The power compensation differential scanning calorimeter of claim 38 , wherein the sample holder contains a sample pan for receiving the sample, and wherein the sample holder has a lid for enclosing the sample inside the sample holder.
45. The power compensation differential scanning calorimeter of claim 38 , wherein the reference holder contains a reference pan for receiving the reference, and wherein the reference holder has a lid for enclosing the reference inside the reference holder.
46. The power compensation differential scanning calorimeter of claim 38 , wherein the sample thermal resistor is a principal path for heat exchange between the sample holder and the isothermal enclosure, and the reference thermal resistor is a principal path for heat exchange between the reference holder and the isothermal enclosure.
47. The power compensation differential scanning calorimeter of claim 38 , wherein the differential heat flow to the sample with respect to the reference is calculated using a five-term heat flow equation.
48. A method for calibrating a power compensation differential scanning calorimeter having an isothermal enclosure containing a sample holder holding a sample and a reference holder holding a reference, the method comprising the steps of:
(a) running a first experiment with the differential scanning calorimeter empty, using a thermal program comprising a first isothermal segment, a second constant heating rate segment, and a third isothermal segment;
(b) running a second experiment with specimens loaded in the sample holder and the reference holder, using the thermal program of the first experiment; and
(c) calculating a sample thermal capacitance, a reference thermal capacitance, a sample thermal resistance, and a reference thermal resistances,
wherein the differential scanning calorimeter is calibrated by calculating the sample thermal capacitance, the reference thermal capacitance, the sample thermal resistance, and the reference thermal resistance.
49. The method of claim 48 , wherein each of the steps of running the first experiment and running the second experiment further comprise:
(i) measuring one of a sample temperature, a reference temperature, and an isothermal enclosure temperature;
(ii) measuring one of a difference between a sample temperature and an isothermal enclosure temperature, a difference between the reference temperature and the isothermal enclosure temperature, and a difference between the sample temperature and the reference temperature;
(iii) measuring another one of the difference between the sample temperature and the reference temperature, the difference between the sample temperature and the isothermal enclosure temperature, and the difference between the reference temperature and the isothermal enclosure temperature; and
(iv) measuring a differential power to a sample with respect to a reference.
50. The method of claim 48 , wherein the first isothermal segment temperature is less than the lowest temperature in a desired temperature calibration range, and the third isothermal segment temperature is greater than the highest temperature in the desired temperature calibration range.
51. The method of claim 48 , wherein the sample thermal capacitance is calculated according to: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · p s1 Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
52. The method of claim 48 , wherein the sample thermal resistance is calculated according to: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · p s1 .
53. The method of claim 48 , wherein the reference thermal capacitance is calculated according to: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · p r1 ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
54. The method of claim 48 , wherein the reference thermal resistance is calculated according to: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) [ m r2 · C mat · ( T s1 d τ - Δ T 1 d τ ) - p r2 ] · ( T s1 d τ - Δ T 1 d τ ) - p r1 · ( Δ T 2 d τ - T s2 d τ ) .
55. A method for calibrating a power compensation differential scanning calorimeter having an isothermal enclosure containing a sample holder holding a sample and a reference holder holding a reference, the method comprising the steps of:
(a) running a first experiment with a first sample specimen in the sample holder and a first reference specimen in the reference holder, using a thermal program comprising a first isothermal segment, a second constant heating rate segment, and a third isothermal segment;
(b) running a second experiment with a second sample specimen in the sample holder and a second reference sample in the reference holder, using the thermal program of the first experiment; and
(c) calculating a sample thermal capacitance, a reference thermal capacitance, a sample thermal resistance, and a reference thermal resistance.
56. The method of claim 55 , wherein the first sample specimen has a mass substantially different than the second sample specimen.
57. The method of claim 55 , wherein the first sample specimen, the first reference specimen, the second sample specimen, and the second reference specimen are sapphire specimens.
58. The method of claim 57 , wherein the sapphire specimens have masses ranging from 25 to 75 mg.
59. The method of claim 55 , wherein sample thermal capacitance is calculated according to: C s = Δ T o1 · ( m s2 · C mat · T s2 d τ - p s2 ) + Δ T o2 · ( p s1 - m s1 · C mat · T s1 d τ ) Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ .
60. The method of claim 55 , wherein sample thermal resistance is calculated according to: R s = Δ T o2 · T s1 d τ - Δ T o1 · T s2 d τ T s1 d τ · ( m s2 · C mat · T s2 d τ - p s2 ) + T s2 d τ · ( p s1 - m s1 · C mat · T s1 d τ ) .
61. The method of claim 55 , wherein reference thermal capacitance is calculated according to: C r = ( Δ T o1 + Δ T 1 ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( Δ T o2 + Δ T 2 ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) .
62. The method of claim 55 , wherein reference thermal resistance is calculated according to: R r = ( Δ T o1 + Δ T 1 ) · ( Δ T 2 d τ - T s2 d τ ) + ( Δ T o2 + Δ T 2 ) · ( T s1 d τ - Δ T 1 d τ ) ( T s1 d τ - Δ T 1 d τ ) · [ m r2 · C mat · ( T s2 d τ - Δ T 2 d τ ) - p r2 ] + ( T s2 d τ - Δ T 2 d τ ) · [ p r1 - m r1 · C mat · ( T s1 d τ - Δ T 1 d τ ) ] .
63. A power compensation differential scanning calorimeter comprising:
(a) an isothermal enclosure;
(b) a sample holder contained in the isothermal enclosure, the sample holder holding a sample;
(c) a reference holder contained in the isothermal enclosure, the reference holder holding a reference;
(d) temperature detectors for measuring an isothermal enclosure temperature, a sample holder temperature, and a reference holder temperature; and
(e) power meters for measuring individually a power supplied to the sample holder and a power supplied to the reference holder,
wherein differential heat flow to the sample with respect to the reference is calculated using a six-term equation as follows: q = p s - p r + T o - T s R s - T o - T r R r - C s · T s d τ + C r · T r d τ .
64. The power compensation differential scanning calorimeter of claim 63 , wherein the power compensation differential scanning calorimeter is calibrated by measuring a sample thermal resistance, a sample thermal capacitance, a reference thermal resistance, and a reference thermal capacitance.
65. The power compensation differential scanning calorimeter of claim 63 , wherein the power compensation differential scanning calorimeter is calibrated by running a first experiment with an empty cell according to a pre-selected temperature program, and running a second experiment, with a sample specimen in the sample holder and a reference specimen in the reference holder, according to the pre-selected temperature program.
66. The power compensation differential scanning calorimeter of claim 63 , wherein the power compensation differential scanning calorimeter is calibrated by running a first experiment with a first sample specimen in the sample holder and a first reference specimen in the reference holder according to a pre-selected temperature program, and running a second experiment, with a second sample specimen in the sample holder and a second reference specimen in the reference holder, according to the pre-selected temperature program, wherein the first sample specimen has a mass that is substantially different from a mass of the second sample specimen.Cited by (0)
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